Step-by-step answer:
Given:
two inequalities:
4-x <= -1 ........................(1)
2+3x >= 17......................(2)
Required: find the solution of the intersection of inequalities.
Solution:
Solution to (1):
4-x <= -1 transpose
4+1 <=x simplify
5 <= x rewrite
x >= 5
Solution to (2)
2+3x >= 17
3x >= 17-2
3x >= 15
x >= 5
The intersection of the two solutions x>=5 and x>=5 is therefore x>=5
Check:
x=4, => 4-4 = 0 >1 so not a solution
x=4, => 2+3(4) = 14 < 17 so not a solution
x=5, => 4-5 = -1 so a solution
x=5, => 2+3(5) = 17, so a solution.
similarly for 6, 7, ....